= Photoemission momentum conversion
{title2=$k_\parallel=\sqrt{2m_eE_{\rm kin}}\sin\theta/\hbar$}
For emission angle $\theta$ measured from the surface normal, a free outgoing <photoelectron> has parallel <wavevector> $k_\parallel=\sqrt{2m_eE_{\rm kin}}\sin\theta/\hbar$. Translation symmetry parallel to a clean periodic surface conserves this component modulo a surface <reciprocal lattice> vector, after accounting for photon momentum when needed. With initial <binding energy> $E_B$ below the <Fermi level>, its kinetic energy immediately outside the sample is $E_{\rm kin}=h\nu-\phi_s-E_B$, where $\phi_s$ is the sample <work function>. This sample-vacuum energy is distinct from the analyzer-referenced energy when contact potentials are present. Perpendicular crystal momentum generally needs a final-state model, whereas a strictly two-dimensional band has no perpendicular dispersion to reconstruct.
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